## Homework, 6th edition, 15.35

$\frac{d[R]}{dt}=-k[R]^{2}; \frac{1}{[R]}=kt + \frac{1}{[R]_{0}}; t_{\frac{1}{2}}=\frac{1}{k[R]_{0}}$

Bianca Barcelo 4I
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### Homework, 6th edition, 15.35

Hi, I was wondering how I would use the second-order reaction (after I found k by using the half-life equation)?
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Christina Chang 1C
Posts: 34
Joined: Thu May 10, 2018 3:00 am

### Re: Homework, 6th edition, 15.35

You are given the [A]0 and you have k, from solving the half-life equation. You are trying to find time and you actually are given [A] as well. For example, in part a) you want to find how long it takes to decrease to one-sixteenth of the original which is [A] and you can figure that out by multiplying 1/16 by the [A]0 to give you [A]. Now you plug everything in to solve for t.

Jim Brown 14B Lec1
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Joined: Fri Sep 28, 2018 12:28 am

### Re: Homework, 6th edition, 15.35

Use the formula t1/2= [A]/2k to solve for k, then modify the formula for the other proportions.
eg.
t1/16= 15[A]/16k
t1/4= 3[A]/4k
etc

Kessandra Ng 1K
Posts: 67
Joined: Fri Sep 28, 2018 12:25 am

### Re: Homework, 6th edition, 15.35

You know the half-life equation for a second-order reaction is: t1/2 = 1 / k [A]o

Therefore, after finding k, you can use the integrated rate law 1/[A] = kt + 1/[A]o for a second-order reaction to find t.